Christmas jerseys: a great intellectual challenge

What would you buy Jeremy Corbyn for Christmas? Printable answers only, please. But somehow, a Christmas jumper seems appropriate. It would match the 1980s-style shell suit he wore the other day. Perhaps one with a portrait of Stalin and the slogan ‘Teacher, Leader, Friend’, a phrase in widespread use in the old Soviet Union, a country he seems to admire. The purchase would help to prop up a declining industry, something which the Labour leader seems keen to do in general.

For the sales of Christmas jerseys have peaked. In 2013, they rose by no less than 450 per cent compared to a year earlier, and this was followed by a further doubling in 2014. This year, according to analysts at WGSN’s INstock service, retailers bought in 10 per cent fewer Christmas woollies than last year. There does seem to be some rational reasons for this decision. A key one is the view taken that the market for these Christmas-themed jerseys was approaching saturation. Outside the festive season, most people shy away from wearing an item of clothing featuring red nosed reindeers or sparkly snowmen. So the old jumper appears from the bottom drawer for its annual outing.

Even so, demand seems to have been even less than anticipated. Some outlets were already marking them down to half price a week ago. It is always easy to be wise after the event. So it was obvious, was it not, that the game was up for these jerseys when Nick Clegg, still then the Deputy Prime Minister, appeared in support of Save the Children sporting a blue number adorned with Christmas puddings. He was, he pronounced on Twitter, ‘hoping to win the office’s most garish jumper competition’. Still, that was possibly one thing he did win.

Many fashion items themselves may be rather trivial, but anticipating tipping points in their life spans is a very demanding intellectual task. How early can we say that a product has reached lift off, and is going to be really popular? Exactly when are we able to pronounce that it is on its way down? Frank Bass, a larger than life Texan professor who used to smoke foot-long cigars, scribbled a few lines of maths down in the early 1960s. He distilled these into a simple non-linear equation – well, simple as far as these things go – and the resulting paper became possibly the most cited in the whole history of marketing science. Bass made a fortune in consultancy fees on the back of it.

Bass relied on dividing consumers into two types, innovators and imitators. His equation described the complex interactions between their behaviours, and tried to estimate their relative importance. This division remains the basis for the even more complicated maths that appears in papers on the topic posted on Cornell’s e-print repository for physics and maths. As a holiday diversion, forget about trying to solve the puzzle which GCHQ released on their Xmas card. Just try and predict the fashion product for next Christmas.